The present invention relates generally to electromagnetic simulation methods and software, and more particularly, to finite difference methods and software that are used for electromagnetic simulation of planar multilayer structures.
A high-performance digital or mixed-signal system can contain thousands of signal lines, which must be routed on several layers in the package and printed circuit board (PCB). These signal layers must be placed between or over power/ground planes in order to have an impedance-controlled board comprising microstrip or stripline transmission lines. A power/ground plane also prevents any coupling of signal lines in an upper layer to signal lines in a lower layer. As a result of this, many power/ground layers have to be included in the stack-up, as shown in FIG. 1. In order to reduce the parasitics of the power delivery network (e.g., to reduce the inductance of the planes), these layers can be allocated to power and ground in an alternating manner such that multiple plane pairs can'exist in a package or board.
Power/ground planes in electronic packaging can be a major factor for noise coupling. There can be noise coupling not only in the transversal direction between two planes, but also in the vertical direction from one plane pair to another through the apertures and via holes. Excessive supply voltage fluctuations cause signal integrity (SI) problems. In addition, noise voltage that gets coupled to the edge of the board may cause significant electromagnetic interference (EMI). Hence, an accurate modeling of power/ground planes is critical to estimate the noise levels especially in mixed-signal systems where high isolation levels are required.
A solid plane made of a perfect conductor of infinite lateral dimensions would completely shield the fields on one side from the other side. Therefore, there would be no need to consider multiple plane pairs. In reality, however, planes at the same dc level have to be connected with vias to each other in order to reduce the effective inductance of the planes. Such a via has to go through a via hole in a plane having a different dc level in order to avoid a short circuit. Through this via and via hole, fields in different plane pairs get coupled to each other. Coupling of multiple plane pairs through such vias has been analyzed using the cavity resonator model by S. Chun, et al., “Modeling of simultaneous switching noise in high speed systems,” IEEE Trans. Adv. Packag., vol. 24, no. 2, pp. 132-142, May 2001, the transmission matrix method by J.-H. Kim and M. Swaminathan, in “Modeling of multilayered power distribution planes using transmission matrix method,” IEEE Trans. Adv. Packag., vol. 25, no. 2, pp. 189-199, May 2002, and coupled transmission lines by H. Wu, et al., “Accurate power supply and ground plane pair models [for MCMs],” IEEE Trans. Adv. Packag., vol. 22, no. 3, pp. 259-266, August 1999.
In addition, planes generally have irregular geometries. There can be large apertures and splits in planes. Fields in different plane pairs can get coupled through these apertures. This can be regarded as a coupling by means of a wrap-around current on the edges of the planes. For narrow slots, a transmission-line-based model has been proposed to take into account this interlayer coupling. See for example, R. Ito et al., “Parallel plate slot coupler modeling using two dimensional frequency domain transmission line matrix method,” in Proc. IEEE EPEP, pp. 41-44, 2004. Electric and magnetic polarization currents have also been considered to compute the coupling through electrically small cutouts. See for example, J. Lee, et al., “Analysis and suppression of SSN noise coupling between power/ground plane cavities through cutouts in multilayer packages and PCBs,” IEEE Trans. Adv. Packag., vol. 28, no. 2, pp 298-309, May 2005.
The field penetration through the conductors can be neglected for frequencies, where the skin depth is much smaller than the plane thickness. At lower frequencies, this field penetration has to be taken into account. See for example, J. Mao, et al., “Modeling of field penetration through planes in multilayered packages,” IEEE Trans. Adv. Packag., vol. 24, no. 3, pp. 326-333, August 2001. For purposes of the description presented below, the thickness of the metal is assumed to be much larger than the skin depth. This assumption is valid above several megahertz for commonly used copper planes in packages.
For modeling of multilayered planes, recently, a method based on the Green's function and segmentation methods including the gap effects has been proposed. See for example, Y. Jeong, et al., “Hybrid analytical modeling method for split power bus in multilayered package,” IEEE Trans. Electromagn. Compat., vol. 48, no. 1, pp. 82-94, February 2006. For realistic structures composed of a large number of layers with many holes and a complicated boundary, a unit-cell-based approach that can be obtained using a finite-difference approximation is more appropriate.
Finite-difference frequency-domain (FDFD) solution of the Helmholtz equation has been recently proposed as a simple and efficient method for modeling of single plane pairs. See for example, O. Ramahi, et al., “A simple finite-difference frequency-domain (FDFD) algorithm for analysis of switching noise in printed circuit boards and packages,” IEEE Trans. Adv. Packag., vol. 26, no. 2, pp. 191-198, May 2003.
Based on the finite-difference method (FDM), two equivalent circuit models for power/ground planes have been developed: T- and X-models. See A. E. Engin, et al., “Finite difference modeling of multiple planes in packages,” presented at the Int. Zurich Symp. Electromagn. Compat., Zurich, Switzerland, February 2006. Also, Engin et al. show a general methodology to combine the frequency response of single plane pairs to obtain a model for multilayered planes taking into account the vertical coupling through the apertures. The multilayered FDM (MFDM) provides a simpler approach without any limit on the number of layers. It provides an accurate representation of wrap-around currents in complicated geometries, which have not been modeled before.
It would be desirable to have methods and software that may be used to model multilayer planes and provide equivalent circuit models for such structures based on multilayer difference methods.